Deriving NOR SR Flip-flop Logic Circuit from Truth Table

Understanding the behavior of a logic circuit, such as the SR (Set-Reset) flip-flop, and translating that behavior into a logical circuit using NOR gates is a fundamental skill in digital electronics. This article will guide you through the process of deriving the NOR SR flip-flop from its truth table and implementing it using logic gates.

Step 1: Understanding the SR Flip-flop

The SR Set-Reset flip-flop is a dual-control edge-triggered flip-flop with two inputs: S (Set) and R (Reset), and two outputs: Q and its complement Q'. The behavior of the SR flip-flop can be described using a truth table:

S R Qnext Q'next 0 0 Q Q' 0 1 0 1 1 0 1 0 1 1 Invalid Invalid

Step 2: Analyzing the Behavior

By examining the truth table, we can deduce the behavior of the flip-flop as follows:

If both S and R are 0, Q remains unchanged. If S is 0 and R is 1, Q is reset to 0. If S is 1 and R is 0, Q is set to 1. If both S and R are 1, the state is invalid.

Step 3: Deriving the Logic Expressions

From the behavior, we can derive the logic expressions that describe the next state of Q and Q':

Qnext S Q ┐R Q'next R Q ┐S

These expressions indicate that:

S will set Q to 1 if S is 1 or Q keeps its current value if S is 0 and R is 0. R will reset Q to 0 if R is 1 or Q keeps its current value if R is 0 and S is 0.

Step 4: Implementing with NOR Gates

The logic expressions can be implemented using NOR gates by simplifying them as follows:

Q S ┐ Q Q' R ┐ Q

This simplification allows us to implement the flip-flop using a NOR gate for each output:

Step 5: Circuit Diagram

The final circuit for the NOR SR flip-flop can be constructed using a series of NOR gates as follows:

Connect the output Q to one input of the first NOR gate and the input S to the other input. Connect the output of the first NOR gate to the input of the second NOR gate along with input R. The output of the second NOR gate gives you Q. Connect Q to the input of the third NOR gate along with R to derive Q'. The output of the third NOR gate gives you Q'.

Note that the design simplifies the implementation by realizing that the same NOR gate configuration can be used for both outputs, with Q being fed back into the gate.

Summary

The NOR SR flip-flop is derived from its truth table by analyzing the behavior of the inputs and outputs, forming logical expressions, and implementing those expressions using NOR gates. The final circuit consists of interconnected NOR gates that maintain the state of Q and Q' based on the inputs S and R.